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Quantitative Methods

Using GAUSS –JORDON Method, find the Inverse of the following matrix :

1 2 -1 4

2 3 2 0

3 1 0 3

2 0 2 1

Quantitative Methods

Given a function described as equation y = 3x + 4, what is y when x is 1, 2, and 3?

Quantitative Methods

(a) Solve the following equation correct to 5 significant figures using Newton’s Method. 4x−sin(x 2 ) +e −2x −x 3 −x 2 +2 = 0 Take the initial guess as x0 = 1.75.

(b) Solve the following equation correct to 5 significant figures using Secant Method. e 2x −x 2 −x−7 = 0 The root must be in the interval [1,1.3].

(c) Solve the following equation correct to 5 significant figures using Bisection Method. x sin(2x) +e 2x +3x−3 = 0 The root must be in the interval [0,0.5].

(d) [ The Newton-Raphson Method ] Perform two iterations to find a real root of the equations y 2 −5y+4 = 0 3yx2 −10x+7 = 0 using the Newton-Rhaphson method and let x0 = y0 = 0.5.

(e) Find a recurrence formula for solving √7 6 and hence approximate its value correct to 5 significant figure. HINT: Apply Newton-Raphson Method

Quantitative Methods

Counting numbes are also called

Quantitative Methods

A researcher collected data on years of education and number of hours spent watching TV per day for a sample of 6 adults:

Years of Education (X)

17, 10, 9, 12, 14, 18

Number of Hours Spent Watching TV Per Day (Y)

1, 4, 6, 5, 3, 2

there a statistically significant correlation between years of education and the number of hours spent watching TV per day? Set α = 0.05.

a. State the Null and Research Hypothesis?

b. Find the critical value?

c. Find the Pearson correlation coefficient? (r value)

e. What is the strength and direction of the correlation?

f. What is the regression equation?

g. Predict the number of hours spent watching TV per day for someone with 11 years of education?

h. What is the coefficient of determination?

Quantitative Methods

Determine the amount of an immediate annuity of N$200 per annum left unpaid for 10 year at 7% p.a compounded interest.

Quantitative Methods

Consumption of sugar-sweetened beverages has increased over the years. Individuals aged 17-20, were surveyed in 2020 across the 10 provinces to determine the number of calories consumed by sugar-sweetened beverages. The average consumption for 17-20-year-old in Canada is 298 calories. You decide to test if the average calorie consumption for students at John Abbott will be less than the national average. You select a random sample of 35 students and your results show that the average sugar-based calorie consumption is 𝑋" = 280, s=18. Do John Abbott students consume significantly fewer sugar-sweetened calories? Set alpha to 0.01 Find Null and research hypothesis 1 or 2 tailed? Find critical value? find test statistic?

Quantitative Methods

Find the inverse of the following Matrix using Gauss Jordan method

1 2 3 0

2 4 3 2

3 2 1 3

6 8 7 5

Quantitative Methods

Find the smallest positive root by using the **bisection method**

**2sin(2x)+2x^3-5**

with **3 decimal plates**

Quantitative Methods

2- The longitudinal extension of metal bar in direction of an applied force is

given by

y = LKeF×1×10−3

Where y is the longitudinal extension in m, L is the length of the bar in m which

is L= 0.15 (m), K is a constant depends on the material and is K= 1, and F is applied

force in N.

a) Find the work done if the force increases from 100 N to 500 N using:

i) An analytical integration technique

ii) A numerical integration technique (n=8 intervals)

[Note: the work done is given by the area under the curve]

b) Using a computer spreadsheet and recalculates step (ii) by increasing

the number of intervals to n=10 and compare your obtained results

with (i) and (ii)

c) Using Simpson’s rule to find the work done (n=8).

d) Analyse whether the size of numerical steps has effect on the obtained

result and explain why.